Answer
a. 1
b. see graph and explanations.
Work Step by Step
a. Since $\lim\limits_{x \to 0}(1-\frac{x^2}{6})=1$, according to the Sandwich Theorem for limits, we have $\lim\limits_{x \to 0}\frac{x\cdot sin(x)}{2-2cos(x)}=1$
b. As can be seen from the graph, all three curves approach 1 when x approaches zero.
The inequalities given in the problem can also be visualized in the graph.
